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Fractional white noise perturbations of parabolic Volterra equations

Sperlich S., Wilke M.

Journal of Applied Analysis

2010

Vol. 16, nr 1

31-48

Aim of this work is to extend the results of Clément, Da Prato and Prüss [5] on the fractional white noise perturbation with Hurst parameter H ∈ (0,1). We will obtain similar results and it will turn out that the regularity of the solution u(t) increases with Hurst parameter H.

Generalized translation operators and Markov processes

Thu N.

Demonstratio Mathematica

2001

Vol. 34, nr 2

295-304

We study the relationship between generalized translation operators and stochastic convolutions on locally compact spaces. We prove that stochastic convolution semigroups can generate Levy type processes which are strong Markov Feller processes and, as an example, we study the Bingham convolution and its dual on integers.